67.1.2 problem 2.2 (b)

Internal problem ID [16267]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 2. Integration and differential equations. Additional exercises. page 32
Problem number : 2.2 (b)
Date solved : Thursday, October 02, 2025 at 10:44:31 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=3-\sin \left (y\right ) \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 22

ode:=diff(y(x),x) = 3-sin(y(x)); 
dsolve(ode,y(x), singsol=all);
 

\[ y = 2 \arctan \left (\frac {2 \sqrt {2}\, \tan \left (\left (c_1 +x \right ) \sqrt {2}\right )}{3}+\frac {1}{3}\right ) \]

✓ Mathematica. Time used: 0.125 (sec). Leaf size: 34

ode=D[y[x],x]==3-Sin[y[x]]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{\sin (K[1])-3}dK[1]\&\right ][-x+c_1]\\ y(x)&\to \arcsin (3) \end{align*}

✓ Sympy. Time used: 1.197 (sec). Leaf size: 41

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(sin(y(x)) + Derivative(y(x), x) - 3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ - \frac {\sqrt {2} \left (\operatorname {atan}{\left (\frac {\sqrt {2} \left (3 \tan {\left (\frac {y{\left (x \right )}}{2} \right )} - 1\right )}{4} \right )} + \pi \left \lfloor {\frac {y{\left (x \right )} - \pi }{2 \pi }}\right \rfloor \right )}{2} = C_{1} - x \]